https://www.explainxkcd.com/wiki/index.php?action=history&feed=atom&title=2545%3A_Bayes%27_Theorem 2026-04-08T02:01:55Z Revision history for this page on the wiki MediaWiki 1.30.0 https://www.explainxkcd.com/wiki/index.php?title=2545:_Bayes%27_Theorem&diff=299628&oldid=prev 2022-11-22T03:12:46Z

<p>‎<span dir="auto"><span class="autocomment">Trivia</span></span></p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr style="vertical-align: top;" lang="en"> <td colspan="2" style="background-color: white; color:black; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: white; color:black; text-align: center;">Revision as of 03:12, 22 November 2022</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l43" >Line 43:</td> <td colspan="2" class="diff-lineno">Line 43:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>**Now this has [https://www.explainxkcd.com/wiki/index.php?title=2545%3A_Bayes%27_Theorem&amp;type=revision&amp;diff=221183&amp;oldid=221182 been fixed] using the &lt;nowiki&gt;&lt;nowiki&gt;&lt;/nowiki&gt; format.</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>**Now this has [https://www.explainxkcd.com/wiki/index.php?title=2545%3A_Bayes%27_Theorem&amp;type=revision&amp;diff=221183&amp;oldid=221182 been fixed] using the &lt;nowiki&gt;&lt;nowiki&gt;&lt;/nowiki&gt; format.</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>***Seems like [[Randall]] made an exploit on himself like [[Mrs. Roberts]] did in [[327: Exploits of a Mom]].</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>***Seems like [[Randall]] made an exploit on himself like [[Mrs. Roberts]] did in [[327: Exploits of a Mom]].</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>***This is extra funny since [[Blondie]]<del class="diffchange diffchange-inline">, </del>is both sometimes used for Mrs Roberts and for Miss Lenhart from this comic.</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>***This is extra funny since [[Blondie]] is both sometimes used for Mrs Roberts and for Miss Lenhart from this comic.</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>{{comic discussion}}</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>{{comic discussion}}</div></td></tr> </table>

Jkshapiro https://www.explainxkcd.com/wiki/index.php?title=2545:_Bayes%27_Theorem&diff=299627&oldid=prev 2022-11-22T03:11:39Z

<p>‎<span dir="auto"><span class="autocomment">Explanation: </span> Removed extraneous paragraph</span></p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr style="vertical-align: top;" lang="en"> <td colspan="2" style="background-color: white; color:black; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: white; color:black; text-align: center;">Revision as of 03:11, 22 November 2022</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l25" >Line 25:</td> <td colspan="2" class="diff-lineno">Line 25:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>In this comic, a teacher is presenting a problem which the students are supposed to use Bayes' theorem to solve. However, the off-panel student knows that they are studying Bayes' theorem, so they use that prior knowledge to guess the usual answer to such problems. The punch line is the caption - The student doesn't need to do the calculation because they're familiar with questions involving Bayes' theorem and how they often present the counterintuitive result to illustrate the importance of prevalence to the calculation.</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>In this comic, a teacher is presenting a problem which the students are supposed to use Bayes' theorem to solve. However, the off-panel student knows that they are studying Bayes' theorem, so they use that prior knowledge to guess the usual answer to such problems. The punch line is the caption - The student doesn't need to do the calculation because they're familiar with questions involving Bayes' theorem and how they often present the counterintuitive result to illustrate the importance of prevalence to the calculation.</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">There is perhaps also a self-referential situation here where the student has updated their prior probabilities a number of times for whether the answer was &quot;Yes&quot; to a question involving Bayes' Theorem. If their method of answering &quot;Yes&quot; to every such question has succeeded every time before then by Bayes' theorem they will have a lot of justification to continue to do until they start getting it wrong. The prevalence of Bayes Theorem questions that require the answer &quot;No&quot; might be small enough that this doesn't happen in any small number of times and so they learn nothing of the false-positive rate until that point in time. This could be interpreted as a criticism of Bayesian Statistics which may treat a judgement as well justified (e.g. getting the question right) despite lacking a clear understanding of mechanism (e.g. basing your answer to the question on the numbers provided). </del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The title text refers to the mathematical definition of Bayes' theorem: P(A | B) = P(B|A) * P(A) / P(B). Here, P(A|B) represents the probability of some event A occurring, given that B has occurred. This is often referred to as &quot;the probability of A given B&quot;. It can be hard to remember if P(A|B) means probability of A given B, or if it's B given A, especially when talking about the probability of an earlier cause given a later effect. Randall's joke is based on this difficulty. Here P((B|A)|(A|B)) is meant to be read as the probability that you ''write'' (B|A) given that the correct expression is (A|B), which makes it the probability that you got the order of the notation mixed up.</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The title text refers to the mathematical definition of Bayes' theorem: P(A | B) = P(B|A) * P(A) / P(B). Here, P(A|B) represents the probability of some event A occurring, given that B has occurred. This is often referred to as &quot;the probability of A given B&quot;. It can be hard to remember if P(A|B) means probability of A given B, or if it's B given A, especially when talking about the probability of an earlier cause given a later effect. Randall's joke is based on this difficulty. Here P((B|A)|(A|B)) is meant to be read as the probability that you ''write'' (B|A) given that the correct expression is (A|B), which makes it the probability that you got the order of the notation mixed up.</div></td></tr> </table>

Jkshapiro https://www.explainxkcd.com/wiki/index.php?title=2545:_Bayes%27_Theorem&diff=299626&oldid=prev 2022-11-22T03:10:12Z

<p>‎<span dir="auto"><span class="autocomment">Explanation</span></span></p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr style="vertical-align: top;" lang="en"> <td colspan="2" style="background-color: white; color:black; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: white; color:black; text-align: center;">Revision as of 03:10, 22 November 2022</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l18" >Line 18:</td> <td colspan="2" class="diff-lineno">Line 18:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|| Total || 1% || 99% || 100%</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|| Total || 1% || 99% || 100%</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|}</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>|}</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>For example, if a test has a 100% sensitivity (first line, all those affected receive a positive result) and a 99% specificity (second line, 1% of the unaffected also receive a positive result), the interpretation of a positive test depends on the prevalence of the disease in the population. In the example case, the prevalence is 0.1% (third column), so that when the test result is positive (1% of the tests, left column) the subject is actually unaffected nine <del class="diffchange diffchange-inline">time </del>out of ten. Although this would be a very performant test, given the relative prevalences involved it will produce overwhelmingly false positives among all positive results. (But, in this example, all those told they are not in danger &amp;mdash; almost a hundred times more individuals than test positive &amp;mdash; are correctly notified.)</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>For example, if a test has a 100% sensitivity (first line, all those affected receive a positive result) and a 99% specificity (second line, 1% of the unaffected also receive a positive result), the interpretation of a positive test depends on the prevalence of the disease in the population. In the example case, the prevalence is 0.1% (third column), so that when the test result is positive (1% of the tests, left column) the subject is actually unaffected nine <ins class="diffchange diffchange-inline">times </ins>out of ten. Although this would be a very performant test, given the relative prevalences involved it will produce overwhelmingly false positives among all positive results. (But, in this example, all those told they are not in danger &amp;mdash; almost a hundred times more individuals than test positive &amp;mdash; are correctly notified.)</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>For this same example, the Bayesian formula gives : &#160;</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>For this same example, the Bayesian formula gives : &#160;</div></td></tr> </table>

Jkshapiro https://www.explainxkcd.com/wiki/index.php?title=2545:_Bayes%27_Theorem&diff=297559&oldid=prev 2022-10-25T09:29:38Z

<p>‎<span dir="auto"><span class="autocomment">Explanation</span></span></p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr style="vertical-align: top;" lang="en"> <td colspan="2" style="background-color: white; color:black; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: white; color:black; text-align: center;">Revision as of 09:29, 25 October 2022</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l8" >Line 8:</td> <td colspan="2" class="diff-lineno">Line 8:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>==Explanation==</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>==Explanation==</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">{{incomplete|Created by &lt;nowiki&gt; P(d/dx x^x|P(d/dx|x^x))) &lt;/nowiki&gt; - Please change this comment when editing this page. Do NOT delete this tag too soon.}}</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>{{w|Bayes' theorem}} describes the probability of an event, given knowledge of conditions related to the event. It is typically used to update the probability that a starting condition occurred, given an outcome. This can reveal unintuitive results when the probability involved is very small. For example, when testing a large number of people for a rare disease, even a fairly accurate test will produce more false positives than the number of people actually afflicted with the disease, and hence a positive result is more likely to be false than true.</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>{{w|Bayes' theorem}} describes the probability of an event, given knowledge of conditions related to the event. It is typically used to update the probability that a starting condition occurred, given an outcome. This can reveal unintuitive results when the probability involved is very small. For example, when testing a large number of people for a rare disease, even a fairly accurate test will produce more false positives than the number of people actually afflicted with the disease, and hence a positive result is more likely to be false than true.</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>{| class=&quot;wikitable&quot;</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>{| class=&quot;wikitable&quot;</div></td></tr> </table>

172.70.218.41 https://www.explainxkcd.com/wiki/index.php?title=2545:_Bayes%27_Theorem&diff=276681&oldid=prev 2022-05-23T18:48:01Z

<p>Reverted edits by <a href="/wiki/index.php/Special:Contributions/Xray_Kilo_Charlie_Delta" title="Special:Contributions/Xray Kilo Charlie Delta">Xray Kilo Charlie Delta</a> (<a href="/wiki/index.php?title=User_talk:Xray_Kilo_Charlie_Delta&amp;action=edit&amp;redlink=1" class="new" title="User talk:Xray Kilo Charlie Delta (page does not exist)">talk</a>) to last revision by <a href="/wiki/index.php/User:Davidy22" title="User:Davidy22">Davidy22</a></p> <a href="//www.explainxkcd.com/wiki/index.php?title=2545:_Bayes%27_Theorem&amp;diff=276681&amp;oldid=274460">Show changes</a>

Jacky720 https://www.explainxkcd.com/wiki/index.php?title=2545:_Bayes%27_Theorem&diff=274460&oldid=prev 2022-05-23T18:15:19Z

<p>haha your js cant stop my js</p> <a href="//www.explainxkcd.com/wiki/index.php?title=2545:_Bayes%27_Theorem&amp;diff=274460&amp;oldid=273167">Show changes</a>

Xray Kilo Charlie Delta https://www.explainxkcd.com/wiki/index.php?title=2545:_Bayes%27_Theorem&diff=273167&oldid=prev 2022-05-21T02:54:43Z

<p>Reverted edits by <a href="/wiki/index.php/Special:Contributions/Explain_xkcd_server_admin" title="Special:Contributions/Explain xkcd server admin">Explain xkcd server admin</a> (<a href="/wiki/index.php?title=User_talk:Explain_xkcd_server_admin&amp;action=edit&amp;redlink=1" class="new" title="User talk:Explain xkcd server admin (page does not exist)">talk</a>) to last revision by <a href="/wiki/index.php/User:Jacky720" title="User:Jacky720">Jacky720</a></p> <a href="//www.explainxkcd.com/wiki/index.php?title=2545:_Bayes%27_Theorem&amp;diff=273167&amp;oldid=271416">Show changes</a>

Davidy22 https://www.explainxkcd.com/wiki/index.php?title=2545:_Bayes%27_Theorem&diff=271416&oldid=prev 2022-05-20T21:49:44Z

<p></p> <a href="//www.explainxkcd.com/wiki/index.php?title=2545:_Bayes%27_Theorem&amp;diff=271416&amp;oldid=263237">Show changes</a>

Explain xkcd server admin https://www.explainxkcd.com/wiki/index.php?title=2545:_Bayes%27_Theorem&diff=263237&oldid=prev 2022-05-04T23:51:11Z

<p>rv</p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr style="vertical-align: top;" lang="en"> <td colspan="2" style="background-color: white; color:black; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: white; color:black; text-align: center;">Revision as of 23:51, 4 May 2022</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1" >Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap 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cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap </del>.;,'&quot;?<del class="diffchange diffchange-inline">!</del>&lt;nowiki&gt;&lt;&gt;{{comic}}<del class="diffchange diffchange-inline">&lt;/nowiki&gt;</del></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">{{comic</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">| number&#160; &#160; = 2545</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">| date&#160; &#160; &#160; = November 22, 2021</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">| title&#160; &#160; = Bayes' Theorem</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">| image&#160; &#160; = bayes_theorem.png</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">| titletext = &lt;nowiki&gt;P((B|A)|(A|B)) represents the probability that you'll mix up the order of the terms when using Bayesian notation.&lt;/nowiki&gt;</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">}}</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">==Explanation==</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">{{incomplete|Created by &lt;nowiki&gt; P(d/dx x^x|P(d/dx|x^x))) &lt;/nowiki&gt; - Please change this comment when editing this page. Do NOT delete this tag too soon.}}</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">{{w|Bayes' theorem}} describes the probability of an event, given knowledge of conditions related to the event. It is typically used to update the probability that a starting condition occurred, given an outcome. This can reveal unintuitive results when the probability involved is very small. For example, when testing a large number of people for a rare disease, even a fairly accurate test will produce more false positives than the number of people actually afflicted with the disease, and hence a positive result is more likely to be false than true.</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">{| class=&quot;wikitable&quot;</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">|| || Tested positive || Tested negative || Total</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">|-</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">|| Affected || 0.1% || 0.0% || 0.1%</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">|-</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">|| Unaffected || 0</ins>.<ins class="diffchange diffchange-inline">9% || 99% || 99.9%</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">|-</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">|| Total || 1% || 99% || 100%</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">|}</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">For example, if a test has a 100% sensitivity (first line, all those affected receive a positive result) and a 99% specificity (second line, 1% of the unaffected also receive a positive result), the interpretation of a positive test depends on the prevalence of the disease in the population. In the example case, the prevalence is 0.1% (third column), so that when the test result is positive (1% of the tests, left column) the subject is actually unaffected nine time out of ten. Although this would be a very performant test, given the relative prevalences involved it will produce overwhelmingly false positives among all positive results. (But, in this example, all those told they are not in danger &amp;mdash</ins>; <ins class="diffchange diffchange-inline">almost a hundred times more individuals than test positive &amp;mdash; are correctly notified.)</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">For this same example, the Bayesian formula gives : </ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">::P( Affected | Positive ) = P( Positive | Affected ) * P( Affected ) / P( Positive ) = 100% * 0.1% / 1% = 10% </ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">::and P( Unaffected | Positive ) = P( Positive | Unaffected ) * P( Unaffected ) / P( Positive ) = 0.9009% * 99.9% / 1% = 90% </ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">In this comic</ins>, <ins class="diffchange diffchange-inline">a teacher is presenting a problem which the students are supposed to use Bayes</ins>' <ins class="diffchange diffchange-inline">theorem to solve. However, the off-panel student knows that they are studying Bayes' theorem, so they use that prior knowledge to guess the usual answer to such problems. The punch line is the caption - The student doesn't need to do the calculation because they're familiar with questions involving Bayes' theorem and how they often present the counterintuitive result to illustrate the importance of prevalence to the calculation.</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">There is perhaps also a self-referential situation here where the student has updated their prior probabilities a number of times for whether the answer was &quot;Yes&quot; to a question involving Bayes' Theorem. If their method of answering &quot;Yes</ins>&quot; <ins class="diffchange diffchange-inline">to every such question has succeeded every time before then by Bayes' theorem they will have a lot of justification to continue to do until they start getting it wrong. The prevalence of Bayes Theorem questions that require the answer &quot;No&quot; might be small enough that this doesn't happen in any small number of times and so they learn nothing of the false-positive rate until that point in time. This could be interpreted as a criticism of Bayesian Statistics which may treat a judgement as well justified (e.g. getting the question right) despite lacking a clear understanding of mechanism (e.g. basing your answer to the question on the numbers provided). </ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">The title text refers to the mathematical definition of Bayes' theorem: P(A | B) = P(B|A) * P(A) / P(B). Here, P(A|B) represents the probability of some event A occurring, given that B has occurred. This is often referred to as &quot;the probability of A given B&quot;. It can be hard to remember if P(A|B) means probability of A given B, or if it's B given A, especially when talking about the probability of an earlier cause given a later effect. Randall's joke is based on this difficulty. Here P((B|A)|(A|B)) is meant to be read as the probability that you ''write'' (B|A) given that the correct expression is (A|B), which makes it the probability that you got the order of the notation mixed up.</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">==Transcript==</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">:[Miss Lenhart is pointing with a pointer, held in her right hand, to a white-board with tables, what looks like formulae and lots of other unreadable text. She looks toward her off-panel class, from where a voice replies to her question.]</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">:Miss Lenhart: Given these prevalences, is it likely that the test result is a false positive?</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">:Off-panel voice: Well, this chapter is on Bayes' Theorem, so yes.</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">:[Caption below the panel]:</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">:Sometimes, if you understand Bayes' Theorem well enough, you don't need it.</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">==Trivia==</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">*When this comic came out, the title text was only &quot;P((B&quot;, and the comic itself linked to [https://xkcd.com/2545/A) A)] or [https://xkcd.com/A) A)] (depending on where the comic was viewed from) and the &quot;Black Lives Matter&quot; image in the header was replaced by &quot;(A&quot;, but this was quickly corrected. </ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">**See this [https://web.archive.org/web/20211122212442/https://xkcd.com/2545/ archived] version.</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">*It turns out that it is the notation that messes with the home page as it also messes with this wiki. </ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">**In this [https://www.explainxkcd.com/wiki/index.php?title=2545:_Bayes%27_Theorem&amp;oldid=221182 version] of this page, the [https://www.explainxkcd.com/wiki/index.php</ins>?<ins class="diffchange diffchange-inline">title=2545%3A_Bayes%27_Theorem&amp;type=revision&amp;diff=221182&amp;oldid=221181 correct title text] has been entered, but it still looked the same so everything from behind the first &quot;|&quot; fails to show.</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">**Now this has [https://www.explainxkcd.com/wiki/index.php?title=2545%3A_Bayes%27_Theorem&amp;type=revision&amp;diff=221183&amp;oldid=221182 been fixed] using the </ins>&lt;nowiki&gt;&lt;<ins class="diffchange diffchange-inline">nowiki</ins>&gt;<ins class="diffchange diffchange-inline">&lt;/nowiki&gt; format.</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">***Seems like [[Randall]] made an exploit on himself like [[Mrs. Roberts]] did in [[327: Exploits of a Mom]].</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">***This is extra funny since [[Blondie]], is both sometimes used for Mrs Roberts and for Miss Lenhart from this comic.</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>{{comic <ins class="diffchange diffchange-inline">discussion</ins>}}</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">[[Category:Comics featuring Miss Lenhart]]</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">[[Category:Statistics]]</ins></div></td></tr> </table>

Jacky720 https://www.explainxkcd.com/wiki/index.php?title=2545:_Bayes%27_Theorem&diff=263205&oldid=prev 2022-05-04T23:51:08Z

<p></p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr style="vertical-align: top;" lang="en"> <td colspan="2" style="background-color: white; color:black; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: white; color:black; text-align: center;">Revision as of 23:51, 4 May 2022</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1" >Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">{{comic</del></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap 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cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap cr​ap </ins>.;,'&quot;?<ins class="diffchange diffchange-inline">!</ins>&lt;nowiki&gt;&lt;&gt;{{comic}}<ins class="diffchange diffchange-inline">&lt;/nowiki&gt;</ins></div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">| number&#160; &#160; = 2545</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">| date&#160; &#160; &#160; = November 22, 2021</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">| title&#160; &#160; = Bayes' Theorem</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">| image&#160; &#160; = bayes_theorem.png</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">| titletext = &lt;nowiki&gt;P((B|A)|(A|B)) represents the probability that you'll mix up the order of the terms when using Bayesian notation.&lt;/nowiki&gt;</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">}}</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">==Explanation==</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">{{incomplete|Created by &lt;nowiki&gt; P(d/dx x^x|P(d/dx|x^x))) &lt;/nowiki&gt; - Please change this comment when editing this page. Do NOT delete this tag too soon.}}</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">{{w|Bayes' theorem}} describes the probability of an event, given knowledge of conditions related to the event. It is typically used to update the probability that a starting condition occurred, given an outcome. This can reveal unintuitive results when the probability involved is very small. For example, when testing a large number of people for a rare disease, even a fairly accurate test will produce more false positives than the number of people actually afflicted with the disease, and hence a positive result is more likely to be false than true.</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">{| class=&quot;wikitable&quot;</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">|| || Tested positive || Tested negative || Total</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">|-</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">|| Affected || 0.1% || 0.0% || 0.1%</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">|-</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">|| Unaffected || 0</del>.<del class="diffchange diffchange-inline">9% || 99% || 99.9%</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">|-</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">|| Total || 1% || 99% || 100%</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">|}</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">For example, if a test has a 100% sensitivity (first line, all those affected receive a positive result) and a 99% specificity (second line, 1% of the unaffected also receive a positive result), the interpretation of a positive test depends on the prevalence of the disease in the population. In the example case, the prevalence is 0.1% (third column), so that when the test result is positive (1% of the tests, left column) the subject is actually unaffected nine time out of ten. Although this would be a very performant test, given the relative prevalences involved it will produce overwhelmingly false positives among all positive results. (But, in this example, all those told they are not in danger &amp;mdash</del>; <del class="diffchange diffchange-inline">almost a hundred times more individuals than test positive &amp;mdash; are correctly notified.)</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">For this same example, the Bayesian formula gives : </del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">::P( Affected | Positive ) = P( Positive | Affected ) * P( Affected ) / P( Positive ) = 100% * 0.1% / 1% = 10% </del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">::and P( Unaffected | Positive ) = P( Positive | Unaffected ) * P( Unaffected ) / P( Positive ) = 0.9009% * 99.9% / 1% = 90% </del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">In this comic</del>, <del class="diffchange diffchange-inline">a teacher is presenting a problem which the students are supposed to use Bayes</del>' <del class="diffchange diffchange-inline">theorem to solve. However, the off-panel student knows that they are studying Bayes' theorem, so they use that prior knowledge to guess the usual answer to such problems. The punch line is the caption - The student doesn't need to do the calculation because they're familiar with questions involving Bayes' theorem and how they often present the counterintuitive result to illustrate the importance of prevalence to the calculation.</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">There is perhaps also a self-referential situation here where the student has updated their prior probabilities a number of times for whether the answer was &quot;Yes&quot; to a question involving Bayes' Theorem. If their method of answering &quot;Yes</del>&quot; <del class="diffchange diffchange-inline">to every such question has succeeded every time before then by Bayes' theorem they will have a lot of justification to continue to do until they start getting it wrong. The prevalence of Bayes Theorem questions that require the answer &quot;No&quot; might be small enough that this doesn't happen in any small number of times and so they learn nothing of the false-positive rate until that point in time. This could be interpreted as a criticism of Bayesian Statistics which may treat a judgement as well justified (e.g. getting the question right) despite lacking a clear understanding of mechanism (e.g. basing your answer to the question on the numbers provided). </del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">The title text refers to the mathematical definition of Bayes' theorem: P(A | B) = P(B|A) * P(A) / P(B). Here, P(A|B) represents the probability of some event A occurring, given that B has occurred. This is often referred to as &quot;the probability of A given B&quot;. It can be hard to remember if P(A|B) means probability of A given B, or if it's B given A, especially when talking about the probability of an earlier cause given a later effect. Randall's joke is based on this difficulty. Here P((B|A)|(A|B)) is meant to be read as the probability that you ''write'' (B|A) given that the correct expression is (A|B), which makes it the probability that you got the order of the notation mixed up.</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">==Transcript==</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">:[Miss Lenhart is pointing with a pointer, held in her right hand, to a white-board with tables, what looks like formulae and lots of other unreadable text. She looks toward her off-panel class, from where a voice replies to her question.]</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">:Miss Lenhart: Given these prevalences, is it likely that the test result is a false positive?</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">:Off-panel voice: Well, this chapter is on Bayes' Theorem, so yes.</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">:[Caption below the panel]:</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">:Sometimes, if you understand Bayes' Theorem well enough, you don't need it.</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">==Trivia==</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">*When this comic came out, the title text was only &quot;P((B&quot;, and the comic itself linked to [https://xkcd.com/2545/A) A)] or [https://xkcd.com/A) A)] (depending on where the comic was viewed from) and the &quot;Black Lives Matter&quot; image in the header was replaced by &quot;(A&quot;, but this was quickly corrected. </del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">**See this [https://web.archive.org/web/20211122212442/https://xkcd.com/2545/ archived] version.</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">*It turns out that it is the notation that messes with the home page as it also messes with this wiki. </del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">**In this [https://www.explainxkcd.com/wiki/index.php?title=2545:_Bayes%27_Theorem&amp;oldid=221182 version] of this page, the [https://www.explainxkcd.com/wiki/index.php</del>?<del class="diffchange diffchange-inline">title=2545%3A_Bayes%27_Theorem&amp;type=revision&amp;diff=221182&amp;oldid=221181 correct title text] has been entered, but it still looked the same so everything from behind the first &quot;|&quot; fails to show.</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">**Now this has [https://www.explainxkcd.com/wiki/index.php?title=2545%3A_Bayes%27_Theorem&amp;type=revision&amp;diff=221183&amp;oldid=221182 been fixed] using the </del>&lt;nowiki&gt;&lt;<del class="diffchange diffchange-inline">nowiki</del>&gt;<del class="diffchange diffchange-inline">&lt;/nowiki&gt; format.</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">***Seems like [[Randall]] made an exploit on himself like [[Mrs. Roberts]] did in [[327: Exploits of a Mom]].</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">***This is extra funny since [[Blondie]], is both sometimes used for Mrs Roberts and for Miss Lenhart from this comic.</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>{{comic <del class="diffchange diffchange-inline">discussion</del>}}</div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&#160;</div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">[[Category:Comics featuring Miss Lenhart]]</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">[[Category:Statistics]]</del></div></td><td colspan="2">&#160;</td></tr> </table>

Ex Kay Cee Dee